### Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates

Here, this study focuses on understanding the phenomena in Monte Carlo simulations known as undersampling, in which Monte Carlo tally estimates may not encounter a sufficient number of particles during each generation to obtain unbiased tally estimates. Steady-state Monte Carlo simulations were performed using the KENO Monte Carlo tools within the SCALE code system for models of several burnup credit applications with varying degrees of spatial and isotopic complexities, and the incidence and impact of undersampling on eigenvalue and flux estimates were examined. Using an inadequate number of particle histories in each generation was found to produce a maximum bias of ~100 pcm in eigenvalue estimates and biases that exceeded 10% in fuel pin flux tally estimates. Having quantified the potential magnitude of undersampling biases in eigenvalue and flux tally estimates in these systems, this study then investigated whether Markov Chain Monte Carlo convergence metrics could be integrated into Monte Carlo simulations to predict the onset and magnitude of undersampling biases. Five potential metrics for identifying undersampling biases were implemented in the SCALE code system and evaluated for their ability to predict undersampling biases by comparing the test metric scores with the observed undersampling biases. Finally, of the five convergence metrics that were investigated, three (the Heidelberger-Welch relative half-width, the Gelman-Rubin

^{$$\hat{R}_c$$}diagnostic, and tally entropy) showed the potential to accurately predict the behavior of undersampling biases in the responses examined.- Publication Date:

- Grant/Contract Number:
- AC05-00OR22725

- Type:
- Accepted Manuscript

- Journal Name:
- Nuclear Science and Engineering

- Additional Journal Information:
- Journal Volume: 185; Journal Issue: 1; Journal ID: ISSN 0029-5639

- Publisher:
- American Nuclear Society - Taylor & Francis

- Research Org:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org:
- USDOE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Monte Carlo; undersampling biases; convergence metrics; SCALE Code System

- OSTI Identifier:
- 1376296

```
Perfetti, Christopher M., Rearden, Bradley T., and Marshall, William J..
```*Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates*. United States: N. p.,
Web. doi:10.13182/NSE16-54.

```
Perfetti, Christopher M., Rearden, Bradley T., & Marshall, William J..
```*Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates*. United States. doi:10.13182/NSE16-54.

```
Perfetti, Christopher M., Rearden, Bradley T., and Marshall, William J.. 2017.
"Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates". United States.
doi:10.13182/NSE16-54. https://www.osti.gov/servlets/purl/1376296.
```

```
@article{osti_1376296,
```

title = {Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates},

author = {Perfetti, Christopher M. and Rearden, Bradley T. and Marshall, William J.},

abstractNote = {Here, this study focuses on understanding the phenomena in Monte Carlo simulations known as undersampling, in which Monte Carlo tally estimates may not encounter a sufficient number of particles during each generation to obtain unbiased tally estimates. Steady-state Monte Carlo simulations were performed using the KENO Monte Carlo tools within the SCALE code system for models of several burnup credit applications with varying degrees of spatial and isotopic complexities, and the incidence and impact of undersampling on eigenvalue and flux estimates were examined. Using an inadequate number of particle histories in each generation was found to produce a maximum bias of ~100 pcm in eigenvalue estimates and biases that exceeded 10% in fuel pin flux tally estimates. Having quantified the potential magnitude of undersampling biases in eigenvalue and flux tally estimates in these systems, this study then investigated whether Markov Chain Monte Carlo convergence metrics could be integrated into Monte Carlo simulations to predict the onset and magnitude of undersampling biases. Five potential metrics for identifying undersampling biases were implemented in the SCALE code system and evaluated for their ability to predict undersampling biases by comparing the test metric scores with the observed undersampling biases. Finally, of the five convergence metrics that were investigated, three (the Heidelberger-Welch relative half-width, the Gelman-Rubin $\hat{R}_c$ diagnostic, and tally entropy) showed the potential to accurately predict the behavior of undersampling biases in the responses examined.},

doi = {10.13182/NSE16-54},

journal = {Nuclear Science and Engineering},

number = 1,

volume = 185,

place = {United States},

year = {2017},

month = {2}

}